What is considered an average or normal bra size for a fourteen year old?

Varies a lot: Almost all girls are "normal" sized (about 95% of healthy people are normal, by definition), but details are hard to come by. For young teen girls, bra sizes can range from about 30 to 36 with cup sizes in the A's and B. The "average" bra size would mean averaging all the bra and cup sizes for all the 14 year old girls in the United States... that answer is unknown.

Breasts: Unlike height and weight, for which there are "norms" - such a strange concept- should anyone be deemed "average" in size? there is no average for breast/bra cup size. The most likely normal is one which is close to other females in your mother's or father's family. Even so, there are tall and short individuals in any family! Breast size is mostly genetically determined.